I'm working on analyzing the measurement equivalence/invariance on a dataset following procedures described in a Vandenberg & Lance (2000) Organizational Research Methods article. I have no problems testing for configural, metric, scalar, or uniqueness invariance, but Vandenberg and Lance recommend beginning with an omnibus test of the equality of covariance matrices across groups.

I'm not precisely sure how to do this in M-plus. I have tried testing a model in which the factor loadings, intercepts, and factor covariances are all constrained to be equal across groups. In looking at my output, I find that the only parameters that differ across groups are factor means. When I attempt to constrain the factor means to be equal across groups (for example, by adding equality constraints in the form of [f01] (75) in MODEL g1 and MODEL g2), my output still shows differences between the factor means of each group.

So, I suppose my question is multifaceted. First, do you have any sense as to whether my approach here will adequately test the equality of the groups' covariance matrices (and if not, do you have any recommendations)? Second, is it necessary to constrain the factor means to be equal (and if so, can you recommend a method for doing so)?